Tagged Questions

Use this tag for questions about specific tensors (curvature tensor, stress tensor), or questions regarding tensor computations as they appear in multivariable calculus and differential/Riemannian geometry (specifically, when it is amenable to be treated as objects with multiple indices that ...

I need to find a real, symmetric matrix, $A$, that satisfies:
$\sum_{i,j} c_i c_j A_{ki}A_{jl} = A_{lk}$
I believe this is an equation of the form:
$c^T B c = A$, where $c$ is $\mathbb{R}^{N \times ...

Being a bit cheeky as I asked this question over on Physics but didn't get a response. http://physics.stackexchange.com/questions/196393/jaumann-deviatoric-stress-rate
Background about terms in this ...

So I'm reading Landau and Lifshitz' Theory of Elasticity (https://archive.org/details/TheoryOfElasticity) and they have done, among (many) other things, something I simply don't understand.
On page ...

Before, I ask similar this. But here I change question settings since it was incomplete. I hope receive good ideas.
Let $E$ be a finite dimensional vector space over field $\mathbb R$ with $E^*$ as ...

Given $f\in C^\infty(U)$, $U$ open set of $\mathbb{R}^n$, we define the differential of $f$ at $p$
$$
(df)_p:T_p\mathbb{R}^n\to\mathbb{R}\\
(df)_p(v):=v(f)
$$
and the differential of $f$
$$
df:U\to ...

Let $M$ be an $n$ dimensional manifold with its bundle of linear frames $\pi:L(M)\to M$. Suppose $T_0$ is a tensor on $\mathbb R^n$ and $u\in L(M)$. We may view $u$ as a linear map $u:\mathbb R^n\to ...

Let $E$ together with $g$ be a inner product space(over field $\mathbb R$) , $\text{dim}E=n<\infty$ and $\{e_1,\cdots,e_n\}$ is orthonormal basis of $E$ that $\{e^1,\cdots,e^n\}$ is its dual basis. ...

I would like to be able to compute a re-ordered kronecker product from the result of another kronecker product. For example, consider $$F=A\otimes B\otimes C\otimes D\otimes E$$ from the result F and ...

My question is two part. First, how does the definition of tensors and tensor spaces change when the vectors that the tensors act upon are elements of a complex vector space as apposed to when they ...

First of all: this is not about the physics behind it. It's about the tensor calculation I've written down below. I know this kind of calculation is exhausting but I would be thankful if someone could ...

Since affine transforms involve a matrix, if the transform matrix is a tensor, it would be of rank two. But, the real question is whether or not a change of basis, or transformation of the underlying ...

Does there exist norms for tensors, as an extension for the ordinary matrix norm?
For example, if there is a derivative of a matrix [A] with respect to a vector {x}, does the norm of this derivative ...

I have a rank 3 tensor $\mathbf{Q}$. What notation should I use to denote the transposition of two of the dimensions?
For instance, if I want to transpose the first and second dimensions, one way I ...